The sharp increase in the total installed capacity of natural gas generators has intensified the dynamic interaction between the electricity and natural gas systems, which could induce cascading failure propagation across the two systems that deserves intensive research. Considering the distinct time response behaviors of the two systems, this paper discusses an integrated simulation approach to simulate the cascading failure propagation process of integrated electricity and natural gas systems (IEGSs). On one hand, considering instantaneous redistribution of power flows after the occurrence of disturbance or failure, the steady-state AC power flow model is employed. On the other hand, gas transmission dynamics are represented by dynamic model to capture the details of its transition process. The interactions between the two systems, intensified by energy coupling components (such as gas-fired generator and electricity-driven gas compressor) as well as the switching among the operation modes of compressors during the cascading failure propagation process, are studied. An IEGS composed of the IEEE 30-bus electricity system and a 14-node 15-pipeline gas system is established to illustrate the effectiveness of the proposed simulation approach, in which two energy subsystems are coupled by compressor and gas-fired generator. Numerical results clearly demonstrate that heterogeneous interactions between electricity and gas systems would trigger the cascading failure propagation between the two coupling systems. Index Terms-Cascading failure propagation, integrated electricity and natural gas system (IEGS), gas compressor, transmission dynamics.